.\"	$OpenBSD: EC_GROUP_new.3,v 1.17 2024/04/27 07:41:47 tb Exp $
.\"	OpenSSL 6328d367 Sat Jul 4 21:58:30 2020 +0200
.\"
.\" This file was written by Matt Caswell <matt@openssl.org>.
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.Dd $Mdocdate: April 27 2024 $
.Dt EC_GROUP_NEW 3
.Os
.Sh NAME
.Nm EC_GROUP_new ,
.Nm EC_GROUP_free ,
.Nm EC_GROUP_clear_free ,
.Nm EC_GROUP_new_curve_GFp ,
.Nm EC_GROUP_new_by_curve_name ,
.Nm EC_GROUP_set_curve ,
.Nm EC_GROUP_get_curve ,
.Nm EC_GROUP_set_curve_GFp ,
.Nm EC_GROUP_get_curve_GFp ,
.Nm EC_get_builtin_curves ,
.Nm EC_curve_nid2nist ,
.Nm EC_curve_nist2nid
.Nd create and destroy EC_GROUP objects
.Sh SYNOPSIS
.In openssl/ec.h
.In openssl/bn.h
.Ft EC_GROUP *
.Fo EC_GROUP_new
.Fa "const EC_METHOD *meth"
.Fc
.Ft void
.Fo EC_GROUP_free
.Fa "EC_GROUP *group"
.Fc
.Ft void
.Fo EC_GROUP_clear_free
.Fa "EC_GROUP *group"
.Fc
.Ft EC_GROUP *
.Fo EC_GROUP_new_curve_GFp
.Fa "const BIGNUM *p"
.Fa "const BIGNUM *a"
.Fa "const BIGNUM *b"
.Fa "BN_CTX *ctx"
.Fc
.Ft EC_GROUP *
.Fo EC_GROUP_new_by_curve_name
.Fa "int nid"
.Fc
.Ft int
.Fo EC_GROUP_set_curve
.Fa "EC_GROUP *group"
.Fa "const BIGNUM *p"
.Fa "const BIGNUM *a"
.Fa "const BIGNUM *b"
.Fa "BN_CTX *ctx"
.Fc
.Ft int
.Fo EC_GROUP_get_curve
.Fa "const EC_GROUP *group"
.Fa "BIGNUM *p"
.Fa "BIGNUM *a"
.Fa "BIGNUM *b"
.Fa "BN_CTX *ctx"
.Fc
.Ft int
.Fo EC_GROUP_set_curve_GFp
.Fa "EC_GROUP *group"
.Fa "const BIGNUM *p"
.Fa "const BIGNUM *a"
.Fa "const BIGNUM *b"
.Fa "BN_CTX *ctx"
.Fc
.Ft int
.Fo EC_GROUP_get_curve_GFp
.Fa "const EC_GROUP *group"
.Fa "BIGNUM *p"
.Fa "BIGNUM *a"
.Fa "BIGNUM *b"
.Fa "BN_CTX *ctx"
.Fc
.Ft size_t
.Fo EC_get_builtin_curves
.Fa "EC_builtin_curve *r"
.Fa "size_t nitems"
.Fc
.Ft "const char *"
.Fo EC_curve_nid2nist
.Fa "int nid"
.Fc
.Ft int
.Fo EC_curve_nist2nid
.Fa "const char *name"
.Fc
.Sh DESCRIPTION
The EC library provides functions for performing operations on
elliptic curves in Weierstrass form.
Such curves are defined over the prime field of order
.Fa p
and satisfy the Weierstrass equation with coefficients
.Fa a
and
.Fa b
.Pp
.Dl y^2 = x^3 + ax + b
.Pp
An
.Vt EC_GROUP
structure is used to represent the definition of an elliptic curve.
A new curve can be constructed by calling
.Fn EC_GROUP_new ,
using the implementation provided by
.Fa meth
(see
.Xr EC_GFp_simple_method 3 ) .
It is then necessary to call
.Fn EC_GROUP_set_curve
to set the curve parameters.
.Pp
.Fn EC_GROUP_set_curve
sets the curve parameters
.Fa p ,
.Fa a ,
and
.Fa b ,
where
.Fa a
and
.Fa b
represent the coefficients of the curve equation.
.Pp
.Fn EC_GROUP_set_curve_GFp
is a deprecated synonym for
.Fn EC_GROUP_set_curve .
.Pp
.Fn EC_GROUP_get_curve
obtains the previously set curve parameters.
.Pp
.Fn EC_GROUP_get_curve_GFp
is a deprecated synonym for
.Fn EC_GROUP_get_curve .
.Pp
The function
.Fn EC_GROUP_new_curve_GFp
is a shortcut for calling
.Fn EC_GROUP_new
and
.Fn EC_GROUP_set_curve .
An appropriate default implementation method will be used.
.Pp
Whilst the library can be used to create any curve using the functions
described above, there are also a number of predefined curves that are
available.
In order to obtain a list of all of the predefined curves, call the
function
.Fn EC_get_builtin_curves .
The parameter
.Fa r
should be an array of
.Vt EC_builtin_cure
structures of size
.Fa nitems .
The function will populate the
.Fa r
array with information about the builtin curves.
If
.Fa nitems
is less than the total number of curves available, then the first
.Fa nitems
curves will be returned.
Otherwise the total number of curves will be provided.
The return value is the total number of curves available (whether that
number has been populated in
.Fa r
or not).
Passing a
.Dv NULL
.Fa r ,
or setting
.Fa nitems
to 0, will do nothing other than return the total number of curves
available.
The
.Vt EC_builtin_curve
structure is defined as follows:
.Bd -literal
typedef struct {
	int nid;
	const char *comment;
} EC_builtin_curve;
.Ed
.Pp
Each
.Vt EC_builtin_curve
item has a unique integer ID
.Pq Fa nid
and a human readable comment string describing the curve.
.Pp
In order to construct a builtin curve, use the function
.Fn EC_GROUP_new_by_curve_name
and provide the
.Fa nid
of the curve to be constructed.
.Pp
.Fn EC_GROUP_free
frees the memory associated with the
.Vt EC_GROUP .
If
.Fa group
is a
.Dv NULL
pointer, no action occurs.
.Pp
.Fn EC_GROUP_clear_free
destroys any sensitive data held within the
.Vt EC_GROUP
and then frees its memory.
If
.Fa group
is a
.Dv NULL
pointer, no action occurs.
.Pp
Some builtin curves can be identified by their NIST name
in addition to a numerical identifier (NID).
.Fn EC_curve_nid2nist
and
.Fn EC_curve_nist2nid
translate between the two.
The five built-in prime curves are:
.Pp
.Bl -column "NIST name" NID_X9_62_prime256v1 "deprecated in SP800-186" -compact
.It No NIST Fa name Ta Em ASN.1 NID       Ta Em notes
.It Qq P-192   Ta Dv NID_X9_62_prime192v1 Ta No deprecated in SP800-186
.It Qq P-224   Ta Dv NID_secp224r1        Ta
.It Qq P-256   Ta Dv NID_X9_62_prime256v1 Ta
.It Qq P-384   Ta Dv NID_secp384r1        Ta
.It Qq P-521   Ta Dv NID_secp521r1        Ta
.El
.Pp
.Fn EC_curve_nid2nist
and
.Fn EC_curve_nist2nid
also accept the ten binary curves defined in FIPS\& 186-4
and deprecated in SP800-186,
although they no longer correspond to builtin curves in LibreSSL.
.Sh RETURN VALUES
All
.Fn EC_GROUP_new*
functions return a pointer to the newly constructed group or
.Dv NULL
on error.
.Pp
.Fn EC_get_builtin_curves
returns the number of builtin curves that are available.
.Pp
.Fn EC_curve_nid2nist
returns a string constant containing the NIST name if
.Fa nid
identifies a NIST curve or
.Dv NULL
otherwise.
.Pp
.Fn EC_curve_nist2nid
returns the NID corresponding to the NIST curve
.Fa name ,
or
.Dv NID_undef .
.Pp
.Fn EC_GROUP_set_curve ,
.Fn EC_GROUP_get_curve ,
.Fn EC_GROUP_set_curve_GFp ,
and
.Fn EC_GROUP_get_curve_GFp
return 1 on success or 0 on error.
.Sh SEE ALSO
.Xr crypto 3 ,
.Xr d2i_ECPKParameters 3 ,
.Xr EC_GFp_simple_method 3 ,
.Xr EC_GROUP_copy 3 ,
.Xr EC_KEY_new 3 ,
.Xr EC_POINT_add 3 ,
.Xr EC_POINT_new 3 ,
.Xr ECDH_compute_key 3 ,
.Xr ECDSA_SIG_new 3
.Sh HISTORY
.Fn EC_GROUP_new ,
.Fn EC_GROUP_free ,
.Fn EC_GROUP_clear_free ,
.Fn EC_GROUP_new_curve_GFp ,
.Fn EC_GROUP_set_curve_GFp ,
and
.Fn EC_GROUP_get_curve_GFp
first appeared in OpenSSL 0.9.7 and have been available since
.Ox 3.2 .
.Pp
.Fn EC_GROUP_new_by_curve_name
and
.Fn EC_get_builtin_curves
first appeared in OpenSSL 0.9.8 and have been available since
.Ox 4.5 .
.Fn EC_curve_nid2nist ,
and
.Fn EC_curve_nist2nid
first appeared in OpenSSL 1.1.0 and have been available since
.Ox 5.8 .
.Pp
.Fn EC_GROUP_set_curve
and
.Fn EC_GROUP_get_curve
first appeared in OpenSSL 1.1.1 and have been available since
.Ox 7.0 .
